This thesis describes the use of adaptive equalization techniques to compensate for the intersymbol interference (ISI) that results when digital data is transmitted over a multipath radio channel. The equalization structures covered in this work are the linear transversal equalizer (LTE), the fractionally spaced equalizer (FSE), the decision-feedback equalizer (DFE), and the maximum-likelihood sequence estimation (MLSE) equalizer. This work also covers adaptive algorithms for equalization including both the least mean squares (LMS) and the recursive least squares (RLS) algorithm. All these equalizer structures and algorithms will be modeled using various simulation modules. Equalization for both stationary and mobile radio channels is considered. Stationary channels are modeled with a simple exponentially decaying profile. The mobile radio channel is represented using a two-ray Rayleigh fading model for an outdoor environment. The SIRCIM channel modeling tool is used to create channel profiles for an indoor mobile radio channel. Adaptive arrays and their similarities to linear equalizers are also studied in this thesis. The properties and performance of simple adaptive array systems using the LMS and RLS algorithms are examined through simulation. This thesis concludes with an in-depth study of the use of adaptive equalization for high-speed data systems operating in an indoor environment. Both stationary and slowly varying radio channels are examined. Simulations of DFE and MLSE equalizers operating in such a system show that both equalizer structures provide better BER performance over a system with no equalization. These simulation results also show that the MLSE equalizer provides better performance than the DFE in almost all cases, but requires a great deal more computations.